You need a newer computer to take advantage of one of Mountain Lion's tastiest treats? Cue the outraged masses: "WTF! Forced obsolesce!" Not so fast, friends. The problem with pre-2011 Macs is that their graphics chipsets don't have the necessary powers for AirPlay mirroring:

It's simple: the secret sauce that Apple requires to make AirPlay Mirroring work is on-GPU H.264 encoding, or the ability to compress video on your device's actual graphic chips without calling upon the CPU.

The great Cult of Mac article points out that Apple requires your graphics card encode the video for your own good. If it didn't, your processor would get so bogged down by the churn that the performance of menus and the like would die. Make sure to check out the whole feature for more video codec nerdery. [Cult of Mac]